Quaternion and Clifford Fourier Transforms and Wavelets

Stephen J. Sangwine

ISBN 10: 3034806027 / ISBN 13: 9783034806022

Editore: Springer Basel, Birkhäuser Basel Jul 2013, 2013

Riguardo questo articolo

Neuware -Quaternion andClifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume presents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamilton¿s quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all its subspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts.This book provides comprehensive insights into current developments and applications including their performance and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms for hypercomplex algebras, which will help readers to see that software implementations are within our grasp.It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms and wavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the contributions that follow relate to each other and to prior work. The book will be a valuable resource for graduate students as well as for scientists and engineers.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 368 pp. Englisch.

Codice articolo 9783034806022

Dati bibliografici

• Titolo: Quaternion and Clifford Fourier Transforms and Wavelets
• Editore: Springer Basel, Birkhäuser Basel Jul 2013
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 3034806027
• ISBN 13: 9783034806022
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 25 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 25 millimetri di profondità
• Peso: 717 grammi

Descrizione articolo

Riassunto

Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume presents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamilton’s quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all its subspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts.

This book provides comprehensive insights into current developments and applications including their performance and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms for hypercomplex algebras, which will help readers to see that software implementations are within our grasp.

It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms and wavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the contributions that follow relate to each other and to prior work. The book will be a valuable resource for graduate students as well as for scientists and engineers.